how can you model the effect of a dilation by a scale factor of 3 on the area of a two dimensional shape?

Answer 1

To model the effect of a dilation by a scale factor of 3 on the area of a two-dimensional shape, you can use the following equation:

New Area = Original Area * (Scale Factor)^2

Here's how it works:

1. Determine the original area of the shape.
2. Square the scale factor (in this case, 3^2 = 9) to account for the two-dimensional aspect.
3. Multiply the original area by the squared scale factor to find the new area.

For example, let's say the original area of a square is 16 square units. With a dilation scale factor of 3, the new area would be:

New Area = 16 * (3^2) = 16 * 9 = 144 square units

Therefore, after a dilation by a scale factor of 3, the original square's area will increase by a factor of 9, resulting in a new area of 144 square units.